4 Boolean Operations Boolean Operation: An operation that manipulates one or more true/false values Specific operations AND OR XOR (exclusive or) NOT

5 The Boolean operations AND, OR, and XOR (exclusive or)

6 Gates Gate: A device that computes a Boolean operation Often implemented as (small) electronic circuits Provide the building blocks from which computers are constructed VLSI (Very Large Scale Integration)

7 A pictorial representation of AND, OR, XOR, and NOT gates

8 Flip-flops Flip-flop: A circuit built from gates that can store one bit. One input line is used to set its stored value to 1 One input line is used to set its stored value to 0 While both input lines are 0, the most recently stored value is preserved

9 A simple flip-flop circuit

10 Setting the output of a flip-flop to 1

11 Setting the output of a flip-flop to 1 (continued)

12 Setting the output of a flip-flop to 1 (continued)

13 Another way of constructing a flip-flop

14 Hexadecimal Notation Hexadecimal notation: A shorthand notation for long bit patterns Divides a pattern into groups of four bits each Represents each group by a single symbol Example: becomes A3

17 Main Memory Cells Cell: A unit of main memory (typically 8 bits which is one byte) Most significant bit: the bit at the left (highorder) end of the conceptual row of bits in a memory cell Least significant bit: the bit at the right (loworder) end of the conceptual row of bits in a memory cell

18 The organization of a byte-size memory cell

19 Main Memory Addresses Address: A name that uniquely identifies one cell in the computer s main memory The names are actually numbers. These numbers are assigned consecutively starting at zero. Numbering the cells in this manner associates an order with the memory cells.

27 Representing Text Each character (letter, punctuation, etc.) is assigned a unique bit pattern. ASCII: Uses patterns of 7-bits to represent most symbols used in written English text (American Standard Code for Information Interchange) ISO developed a number of 8 bit extensions to ASCII, each designed to accommodate a major language group (International Organization for Standardization) Unicode: Uses patterns of 16-bits to represent the major symbols used in languages world wide

30 Representing Numeric Values Binary notation: Uses bits to represent a number in base two Limitations of computer representations of numeric values Overflow: occurs when a value is too big to be represented Truncation: occurs when a value cannot be represented accurately

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